Preferential duplication graphs

Preferential duplication graphs

Netta Cohen, Jonathan Jordan, and Margaritis Voliotis

Source: J. Appl. Probab. Volume 47, Number 2 (2010), 572-585.

Abstract

We consider a preferential duplication model for growing random graphs, extending previous models of duplication graphs by selecting the vertex to be duplicated with probability proportional to its degree. We show that a special case of this model can be analysed using the same stochastic approximation as for vertex-reinforced random walks, and show that `trapping' behaviour can occur, such that the descendants of a particular group of initial vertices come to dominate the graph.

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Primary Subjects: 05C80

Secondary Subjects: 60G99, 60K35

Keywords: Preferential duplication graphs; stochastic approximation; vertex-reinforced random walk

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jap/1276784910
Digital Object Identifier: doi:10.1239/jap/1276784910
Zentralblatt MATH identifier: 05758488
Mathematical Reviews number (MathSciNet): MR2668507

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